IDEAS home Printed from https://ideas.repec.org/a/eee/reensy/v138y2015icp54-58.html
   My bibliography  Save this article

On the optimal degree of imperfect repair

Author

Listed:
  • Finkelstein, Maxim

Abstract

A simple cost-wise comparison between the minimal and perfect repair of a system is discussed first using a relevant example. The main focus of this note, however, is on imperfect (general) repair. The best repair for our system in this case is defined as the one that corresponds to the optimal level (extent) of repair actions that minimize the long-run expected cost per unit of time. This complex optimization problem is considered for a specific imperfect repair model (Kijima II), using the developed earlier asymptotic approach to the corresponding virtual age modelling. It is shown that the optimal solution exists when the failure rate of a system tends to infinity as t tends to infinity and the corresponding cost function decreases sufficiently fast. An example illustrating the optimization procedure is considered.

Suggested Citation

  • Finkelstein, Maxim, 2015. "On the optimal degree of imperfect repair," Reliability Engineering and System Safety, Elsevier, vol. 138(C), pages 54-58.
    • Handle: RePEc:eee:reensy:v:138:y:2015:i:c:p:54-58
    DOI: 10.1016/j.ress.2015.01.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0951832015000204
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ress.2015.01.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Tanwar, Monika & Rai, Rajiv N. & Bolia, Nomesh, 2014. "Imperfect repair modeling using Kijima type generalized renewal process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 24-31.
    2. Pham, Hoang & Wang, Hongzhou, 1996. "Imperfect maintenance," European Journal of Operational Research, Elsevier, vol. 94(3), pages 425-438, November.
    3. Scarsini, Marco & Shaked, Moshe, 2000. "On the value of an item subject to general repair or maintenance," European Journal of Operational Research, Elsevier, vol. 122(3), pages 625-637, May.
    4. Finkelstein, Maxim & Ludick, Zani, 2014. "On some steady-state characteristics of systems with gradual repair," Reliability Engineering and System Safety, Elsevier, vol. 128(C), pages 17-23.
    5. Hongzhou Wang & Hoang Pham, 2006. "Reliability and Optimal Maintenance," Springer Series in Reliability Engineering, Springer, number 978-1-84628-325-3, January.
    6. Toshio Nakagawa, 2008. "Advanced Reliability Models and Maintenance Policies," Springer Series in Reliability Engineering, Springer, number 978-1-84800-294-4, January.
    7. Shafiee, Mahmood & Finkelstein, Maxim & Chukova, Stefanka, 2011. "On optimal upgrade level for used products under given cost structures," Reliability Engineering and System Safety, Elsevier, vol. 96(2), pages 286-291.
    8. Kahle, Waltraud, 2007. "Optimal maintenance policies in incomplete repair models," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 563-565.
    9. Finkelstein, Maxim, 2007. "On statistical and information-based virtual age of degrading systems," Reliability Engineering and System Safety, Elsevier, vol. 92(5), pages 676-681.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Liu, Xingheng & Vatn, Jørn & Dijoux, Yann & Toftaker, Håkon, 2020. "Unobserved heterogeneity in stable imperfect repair models," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    2. Nguyen, Dinh Tuan & Dijoux, Yann & Fouladirad, Mitra, 2017. "Analytical properties of an imperfect repair model and application in preventive maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 256(2), pages 439-453.
    3. Liu, Xingheng & Finkelstein, Maxim & Vatn, Jørn & Dijoux, Yann, 2020. "Steady-state imperfect repair models," European Journal of Operational Research, Elsevier, vol. 286(2), pages 538-546.
    4. Aghezzaf, El-Houssaine & Khatab, Abdelhakim & Tam, Phuoc Le, 2016. "Optimizing production and imperfect preventive maintenance planning׳s integration in failure-prone manufacturing systems," Reliability Engineering and System Safety, Elsevier, vol. 145(C), pages 190-198.
    5. de Jonge, Bram & Scarf, Philip A., 2020. "A review on maintenance optimization," European Journal of Operational Research, Elsevier, vol. 285(3), pages 805-824.
    6. Ait Mokhtar, El Hassene & Laggoune, Radouane & Chateauneuf, Alaa, 2023. "Imperfect maintenance modeling and assessment of repairable multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 234(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Maxim Finkelstein & Mahmood Shafiee, 2017. "Preventive maintenance for systems with repairable minor failures," Journal of Risk and Reliability, , vol. 231(2), pages 101-108, April.
    2. Shafiee, Mahmood & Chukova, Stefanka, 2013. "Maintenance models in warranty: A literature review," European Journal of Operational Research, Elsevier, vol. 229(3), pages 561-572.
    3. Tanwar, Monika & Rai, Rajiv N. & Bolia, Nomesh, 2014. "Imperfect repair modeling using Kijima type generalized renewal process," Reliability Engineering and System Safety, Elsevier, vol. 124(C), pages 24-31.
    4. Nguyen, Dinh Tuan & Dijoux, Yann & Fouladirad, Mitra, 2017. "Analytical properties of an imperfect repair model and application in preventive maintenance scheduling," European Journal of Operational Research, Elsevier, vol. 256(2), pages 439-453.
    5. Lo, Hui-Chiung & Yu, Rouh-Yun, 2013. "A study of quality management strategy for reused products," Reliability Engineering and System Safety, Elsevier, vol. 119(C), pages 172-177.
    6. Chaabane, K. & Khatab, A. & Diallo, C. & Aghezzaf, E.-H. & Venkatadri, U., 2020. "Integrated imperfect multimission selective maintenance and repairpersons assignment problem," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    7. Maxim Finkelstein & Gregory Levitin & Oleg A Stepanov, 2019. "On operation termination for degrading systems with two types of failures," Journal of Risk and Reliability, , vol. 233(3), pages 419-426, June.
    8. Taghipour, Sharareh & Banjevic, Dragan, 2012. "Optimal inspection of a complex system subject to periodic and opportunistic inspections and preventive replacements," European Journal of Operational Research, Elsevier, vol. 220(3), pages 649-660.
    9. Taghipour, Sharareh & Banjevic, Dragan & Jardine, Andrew K.S., 2010. "Periodic inspection optimization model for a complex repairable system," Reliability Engineering and System Safety, Elsevier, vol. 95(9), pages 944-952.
    10. Hashemi, M. & Asadi, M. & Zarezadeh, S., 2020. "Optimal maintenance policies for coherent systems with multi-type components," Reliability Engineering and System Safety, Elsevier, vol. 195(C).
    11. Izquierdo, J. & Márquez, A. Crespo & Uribetxebarria, J. & Erguido, A., 2020. "On the importance of assessing the operational context impact on maintenance management for life cycle cost of wind energy projects," Renewable Energy, Elsevier, vol. 153(C), pages 1100-1110.
    12. Maxim Finkelstein & Ji Hwan Cha, 2022. "Reducing degradation and age of items in imperfect repair modeling," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1058-1081, December.
    13. Ammar Y. Alqahtani & Surendra M. Gupta, 2017. "One-Dimensional Renewable Warranty Management within Sustainable Supply Chain," Resources, MDPI, vol. 6(2), pages 1-26, April.
    14. Sergey S. Ketkov & Oleg A. Prokopyev & Lisa M. Maillart, 2023. "Planning of life-depleting preventive maintenance activities with replacements," Annals of Operations Research, Springer, vol. 324(1), pages 1461-1483, May.
    15. Ait Mokhtar, El Hassene & Laggoune, Radouane & Chateauneuf, Alaa, 2023. "Imperfect maintenance modeling and assessment of repairable multi-component systems," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    16. Nguyen, Kim-Anh & Do, Phuc & Grall, Antoine, 2017. "Joint predictive maintenance and inventory strategy for multi-component systems using Birnbaum’s structural importance," Reliability Engineering and System Safety, Elsevier, vol. 168(C), pages 249-261.
    17. Toon Vanderschueren & Robert Boute & Tim Verdonck & Bart Baesens & Wouter Verbeke, 2022. "Prescriptive maintenance with causal machine learning," Papers 2206.01562, arXiv.org.
    18. Young Yun, Won & Nakagawa, Toshio, 2010. "Replacement and inspection policies for products with random life cycle," Reliability Engineering and System Safety, Elsevier, vol. 95(3), pages 161-165.
    19. Badía, F.G. & Berrade, M.D. & Cha, Ji Hwan & Lee, Hyunju, 2018. "Optimal replacement policy under a general failure and repair model: Minimal versus worse than old repair," Reliability Engineering and System Safety, Elsevier, vol. 180(C), pages 362-372.
    20. Serguei Maximov & Consuelo de J. Cortes-Penagos, 2020. "A long-time asymptotic solution to the g-renewal equation for underlying distributions with nondecreasing hazard functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 92(2), pages 311-341, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:reensy:v:138:y:2015:i:c:p:54-58. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/reliability-engineering-and-system-safety .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.